The set of all x for which f(x)= log (x-2/x+3) 2 and g(x)=(1/√x2-9) are both not defined is

Question

The set of all x for which f(x)= log (x-2/x+3) 2 and g(x)=(1/√x2-9) are both not defined is (A) (-3,2) (B) [-3,2) (C) (-3,2] (D) [-3,2]

Tardigrade Admin · Accepted Answer

The function f is not defined for -3 ≤ x ≤ 2 and g is not defined for those x for which x2-9 ≤ 0 i.e., x ∈[-3,3]. Thus f and g are not defined on [-3,2].

Q. The set of all $x$ for which $f (x) = lo g_{\frac{x - 2}{x + 3}} 2$ and $g (x) = \frac{1}{x ^{2} - 9}$ are both not defined is

$(- 3, 2)$

$[- 3, 2)$

$(- 3, 2]$

$[- 3, 2]$

The function $f$ is not defined for $- 3 \leq x \leq$ 2 and $g$ is not defined for those $x$ for which $x^{2} - 9 \leq 0$ i.e., $x \in [- 3, 3]$ .
Thus $f$ and $g$ are not defined on $[- 3, 2]$ .

Q. The set of all x for which f(x)=logx+3x−2​​2 and g(x)=x2−9​1​ are both not defined is

(−3,2)

[−3,2)

(−3,2]

[−3,2]